Question: Given $ m \angle MON = 2x + 23$, $ m \angle LOM = 9x - 1$, and $ m \angle LON = 66$, find $m\angle MON$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {9x - 1} + {2x + 23} = {66}$ Combine like terms: $ 11x + 22 = 66$ Subtract $22$ from both sides: $ 11x = 44$ Divide both sides by $11$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 2({4}) + 23$ Simplify: $ {m\angle MON = 8 + 23}$ So ${m\angle MON = 31}$.